STA 293 B: MULTISCALE METHODS
STATISTICS IN TIME/FREQUENCY AND TIME/SCALE DOMAINS
Support/Demos/Practice
WaveLab 0.8
Time-Frequency Toolbox
Credit where credit is due!
Some of the M-files below are modifications of various Workout and Demo files from
WaveLab 0.8 and Time-Frequency Toolbox.
Thanks to numerous contributors to both projects.
Class 1: Intro
Class 2: Demo 0-2
dwt.m Bare-Bone DWT.
demo0.m
demo1.m
demo2.m
Class 3: Wavelets and Their Construction.
demo3.m
Constructing wavelets in the Fourier Domain.
Needs: m0.m.
It might be useful to refresh the
Fourier Transform.
Class 4: In the wavelet forest...(en la selva de onduletas).
HW1
Class 5: Wavelet Packets
Codes from the handout.
packet1.m Daub2 Wavelet Packet Functions
packet2.m
packet3.m Famous MishMash!
packet4.m Mallat and Zhang's
Transients (a synthetic signal).
Class 6: TFTB Package
(Gabor, Wigner-Ville and Cohen's Class Time Frequency Representations)
spect1.m Spectrogram of a Nasty Chirp.
A couple of messy handouts :
hand1.ps and
hand2.ps as well as
supporting M files: tf1.m ,
tf15.m ,
tf2.m ,
tf3.m .
For more details see Mallat's bible:
Wavelet Tour of Signal Processing and
the part of WaveLab [books/WaveTour] related to the book.
Class 7,8: Wavelet Research at ISDS.
Check DP page by
entering key-words wavelet or
wavelets.
Class 9: Hidden Markov Trees (HMT) in the wavelet domain
DSP group
at Rice is the authority on HMT wavelet modeling.
Some of their publications can be found at
http://www.dsp.rice.edu/publications/#waveletDSP page.
In this class we will discuss paper:
J. K. Romberg, H. Choi and R. G. Baraniuk,
Bayesian Wavelet Domain Image Modeling using Hidden Markov Trees
to appear in Proc. IEEE International Conference on Image Processing
DSP folks also developed a MATLAB denoiser based on HMT models.
It works well but it is slow when the input image is large.
Check their SOFTWARE
page.
Slides From The Final Exam Presentations
Rui Paulo
Rui's Hypotheses concerning the density phi squared
Check: landscape slides
and portrait slides.
Contact Rui at rui@isds.duke.edu
if interested/or have solution of this problem.
Theory
Scale/Space Methods
- Flandrin's classification.
- Fourier Methods
- Gabor-type Methods, Gabor Transformation,
- Wigner-Ville Paradigm, Bilinear Classes, Cohen Classes
Wavelets
- Continuous Wavelet Transformations
- Critically Sampled Wavelet Transformations
- Wavelet Packets, Stationary Wavelet Transformations
- Swelden's Lifting Scheme
- Mallat-Carmona's Ridges Paradigm
Pursuit Methods
Applications
- Bayesian Shrinkage Galore
- Density Estimation -- Why? How?
- Time series in the wavelet domain
- Katul's Wavelet Measures, Townsend's decompositions
- Filtering turbulence signals (A la Steve Lalley's
title of his Annals of Statistics paper [AOS, 27, 461]:
BENEATH THE NOISE, CHAOS!)
- Multifractal turbulence models and K41 theory.
Text:
B. Vidakovic,
Statistical Modeling By Wavelets, Wiley, 1999 [ISBN 0-471-29365-2]
Recommended Reading:
[1] P. Flandrin,
Time-Frequency/Time Scale Analysis, Academic Press, 1999 [ISBN 0-12-259870-9]
[2] G. G. Walter, Wavelets and other orthogonal systems with
applications, CRC, 1994 [ISBN 0-8493-7878-8]
Instructor's Notes and Handouts